Back to Classics: Teaching Limits Through Infinitesimals
نویسنده
چکیده
The usual E, δ-definition of the limit of a function (whether pre sented at a rigorous or an intuitive level) requires a “candidate L” for the limit value. Thus, we have to start our first calculus course with “guessing” instead of “calculating”. In this paper we criticize the method of using calculators for the purpose of selecting candidates for L. We suggest an alternative: a working formula for calculating the limit value L of a real function in terms of infinitesimals. Our for mula, if considered as a definition of limit, is equivalent to the usual E, δ-definition but does not involve a candidate L for the limit value. As a result, the Calculus becomes to “calculate” again as it was orig inally designed to do.
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Teaching Calculus with Infinitesimals
Synopsis This article argues that first semester calculus courses for non-mathematics majors should be taught using infinitesimals. This applies to both high school and undergraduate calculus courses. The use of infinitesimals in calculus, though more intuitive than the approach developed in the 19 th century, has been controversial for over two millennia. However, in the 20 th century their us...
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